Solve sqrt{(-2)^2}=|-1|+1/9x(-3)^2+sqrt[3]{-8}

$$\sqrt { ( - 2 ) ^ { 2 } } = | - 1 | + \frac { 1 } { 9 } x ( - 3 ) ^ { 2 } + \sqrt[ 3 ] { - 8 }$$

Solve for x (complex solution)

$$x=2e^{\frac{5\pi i}{3}}-1\approx 2.220446049 \cdot 10^{-16}-1.732050808i$$

Steps for Solving Linear Equation

Calculate -2 to the power of 2 and get 4.

$$\sqrt{4}=|-1|+\frac{1}{9}x\left(-3\right)^{2}+\sqrt[3]{-8}$$

Calculate the square root of 4 and get 2.

$$2=|-1|+\frac{1}{9}x\left(-3\right)^{2}+\sqrt[3]{-8}$$

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of -1 is 1.

$$2=1+\frac{1}{9}x\left(-3\right)^{2}+\sqrt[3]{-8}$$

Calculate -3 to the power of 2 and get 9.

$$2=1+\frac{1}{9}x\times 9+\sqrt[3]{-8}$$

Multiply \frac{1}{9} and 9 to get 1.

$$2=1+x+\sqrt[3]{-8}$$

Swap sides so that all variable terms are on the left hand side.

$$1+x+\sqrt[3]{-8}=2$$

Subtract 1 from both sides.

$$x+\sqrt[3]{-8}=2-1$$

Subtract 1 from 2 to get 1.

$$x+\sqrt[3]{-8}=1$$

Subtract \sqrt[3]{-8} from both sides.

$$x=1-\sqrt[3]{-8}$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Calculate -2 to the power of 2 and get 4.

$$\sqrt{4}=|-1|+\frac{1}{9}x\left(-3\right)^{2}+\sqrt[3]{-8}$$

Calculate the square root of 4 and get 2.

$$2=|-1|+\frac{1}{9}x\left(-3\right)^{2}+\sqrt[3]{-8}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -1 is 1.

$$2=1+\frac{1}{9}x\left(-3\right)^{2}+\sqrt[3]{-8}$$

Calculate -3 to the power of 2 and get 9.

$$2=1+\frac{1}{9}x\times 9+\sqrt[3]{-8}$$

Multiply \frac{1}{9} and 9 to get 1.

$$2=1+x+\sqrt[3]{-8}$$

Calculate \sqrt[3]{-8} and get -2.

$$2=1+x-2$$

Subtract 2 from 1 to get -1.

$$2=-1+x$$

Swap sides so that all variable terms are on the left hand side.

$$-1+x=2$$

Add 1 to both sides.

$$x=2+1$$

Add 2 and 1 to get 3.

$$x=3$$